# 4.5 Graphs of Sine and Cosine Functions

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4.5 Graphs of Sine and Cosine Functions
Students will sketch the graphs of basic sine and cosine functions. Students will use amplitude and period to help sketch the graphs of sine and cosine functions. Students will sketch translations of graphs of sine and cosine functions. Students will use sine and cosine functions to model real-life data.

Evaluate the Sine Curve using the unit circle

x y (0, 1) 90° 120° 60° 135° 45° 30° 150° (–1, 0) 180° (1, 0) 210° 330° 315° 225° 240° 300° (0, –1) 270°

The Sine Curve

Evaluate the Cosine Curve using the unit circle

x y (0, 1) 90° 120° 60° 135° 45° 30° 150° (–1, 0) 180° (1, 0) 210° 330° 315° 225° 240° 300° (0, –1) 270°

The Cosine Curve

Section 4.5, Figure 4.44, Key Points in the Sine and Cosine Curves, pg. 288

Graph y = sin x and y = 2 sin x on your graphing calculator
Graph y = sin x and y = 2 sin x on your graphing calculator. Notice that the height of the hump has changed. In the equation y = a sin x is known as the amplitude of the function.

Graph y = cos x and y = cos 2x on your graphing calculator
Graph y = cos x and y = cos 2x on your graphing calculator. Notice that the length of the curve has changed. In the equation y = cos bx, b affects the period of the function. Using sin and cos

Find the period and amplitude

Find the period and amplitude

Describe the relationship between the graphs of f and g
Describe the relationship between the graphs of f and g. Consider amplitudes, periods, and shifts. p. 294 #15

Describe the relationship between the graphs of f and g
Describe the relationship between the graphs of f and g. Consider amplitudes, periods, and shifts. p. 294 #21

Sketch the graphs of f and g in the same coordinate plane
Sketch the graphs of f and g in the same coordinate plane. (Include two full periods.) p. 294 #27

Reference Graphs y = sin x y = cos x